Patent application title: Sifting Models of a Subsurface Structure

Abstract:

Multiple models are generated based on information relating to
uncertainties of model parameters, where the models are consistent with
preexisting data regarding a subsurface structure. A system receives, on
a continual basis, information collected as an operation is performed
with respect to the subsurface structure. The multiple models are
recursively sifted to progressively select smaller subsets of the models
as the collected information is continually received.

Claims:

1. A method comprising: generating, by a system having a processor, a
plurality of models of a subsurface structure based on information
relating to uncertainties of model parameters, wherein the plurality of
models are consistent with preexisting data regarding the subsurface
structure; receiving, by the system on a continual basis, information
collected as an operation is performed with respect to the subsurface
structure; and recursively sifting the plurality of models to
progressively select smaller numbers of the plurality of models as the
collected information is continually received.

2. The method of claim 1, wherein receiving the collected information
comprises receiving the collected information as a well is drilled into
the subsurface structure.

3. The method of claim 1, wherein generating the plurality of models
comprises generating anisotropic models of the subsurface structure.

5. The method of claim 1, wherein recursively sifting the plurality of
models comprises: associating marker horizons with the corresponding ones
of the plurality of models; as the collected information is received,
comparing the marker horizons to actual locations of elements in the
subsurface structure; and based on the comparing, progressively
eliminating ones of the plurality of models.

6. The method of claim 1, wherein recursively sifting the plurality of
models comprises: associating modeled travel times of signals in
corresponding ones of the plurality of models; as the collected
information is received, comparing the modeled travel times to actual
travel times of signals; and based on the comparing, progressively
eliminating ones of the plurality of models.

7. The method of claim 1, wherein generating the plurality of models is
based on performing an uncertainty analysis.

8. The method of claim 7, wherein performing the uncertainty analysis is
based on a covariance matrix that represents the uncertainties of model
parameters.

10. The method of claim 1, wherein the preexisting data comprises survey
data collected by survey equipment located at or above a surface above
the subsurface structure.

11. The method of claim 10, wherein the survey data comprises one or more
of seismic data or electromagnetic data.

12. An article comprising at least one machine-readable storage medium
storing instructions that upon execution cause a system having a
processor to: receive survey data regarding a subsurface structure
collected by survey equipment; generate a plurality of models of the
subsurface structure based on information relating to uncertainties of
model parameters, wherein the plurality of models are consistent with the
survey data; receive, on a continual basis, information collected as an
operation is performed with respect to the subsurface structure; and
recursively sift the plurality of models to progressively select smaller
numbers of the plurality of models as the collected information is
continually received.

13. The article of claim 12, wherein the survey data comprises one or
more of seismic survey data and electromagnetic survey data.

14. The article of claim 13, wherein receiving the information comprises
receiving data collected by a logging tool in a well.

15. The article of claim 14, wherein the operation performed with respect
to the subsurface structure is a drilling operation to drill the well.

16. The article of claim 12, wherein recursively sifting the plurality of
models comprises: associating marker horizons with the corresponding ones
of the plurality of models; as the collected information is received,
comparing the marker horizons to actual locations of elements in the
subsurface structure; and based on the comparing, progressively
eliminating ones of the plurality of models.

17. The article of claim 12, wherein recursively sifting the plurality of
models comprises: associating modeled travel times of signals in
corresponding ones of the plurality of models; as the collected
information is received, comparing the modeled travel times to actual
travel times of signals; and based on the comparing, progressively
eliminating ones of the plurality of models.

18. A system comprising: a storage media to store survey data regarding a
subterranean structure; and at least one processor configured to:
generate a plurality of models of the subsurface structure based on
information relating to uncertainties of model parameters, wherein the
plurality of models are consistent with the survey data; receive, on a
continual basis, information collected as an operation is performed with
respect to the subsurface structure; and recursively sift the plurality
of models to progressively select smaller numbers of the plurality of
models as the collected information is continually received.

19. The system of claim 18, wherein to recursively sift the plurality of
models, the at least one processor is configured to further: associate
marker horizons with the corresponding ones of the plurality of models;
as the collected information is received, compare the marker horizons to
actual locations of elements in the subsurface structure; and based on
the comparing, progressively eliminate ones of the plurality of models.

20. The system of claim 18, wherein to recursively sift the plurality of
models, the at least one processor is configured to: associate modeled
travel times of signals in corresponding ones of the plurality of models;
as the collected information is received, compare the modeled travel
times to actual travel times of signals; and based on the comparing,
progressively eliminate ones of the plurality of models.

[0002] This application is related to U.S. application Ser. No.
12/354,548, filed Jan. 15, 2009, U.S. Patent Publication No.
2009/0184958, which is hereby incorporated by reference.

BACKGROUND

[0003] Various techniques (e.g., electromagnetic or seismic techniques)
exist to perform surveys of a subsurface structure for identifying
subsurface elements of interest. Examples of subsurface elements of
interest in the subsurface structure include hydrocarbon-bearing
reservoirs, gas injection zones, thin carbonate or salt layers,
fresh-water aquifers, and so forth.

[0004] One type of electromagnetic (EM) survey technique is the controlled
source electromagnetic (CSEM) survey technique, in which an
electromagnetic transmitter, called a "source," is used to generate
electromagnetic signals. Surveying units, called "receivers," are
deployed on a surface (such as at the sea floor or on land) within an
area of interest to make measurements from which information about the
subsurface structure can be derived. The receivers may include a number
of sensing elements for detecting any combination of electric fields,
electric currents, and/or magnetic fields.

[0005] A seismic survey technique uses a seismic source, such as an air
gun, a vibrator, or an explosive to generate seismic waves. The seismic
waves are propagated into the subsurface structure, with a portion of the
seismic waves reflected back to the surface (earth surface, sea floor,
sea surface, or wellbore surface) for receipt by seismic receivers (e.g.,
geophones, hydrophones, etc.).

[0006] Measurement data (e.g., seismic measurement data or EM measurement
data) can be analyzed to develop a model of a subsurface structure. The
model can include, as examples, a velocity profile (in which velocities
at different points in the subsurface structure are derived), a density
profile, an electrical conductivity profile, and so forth.

SUMMARY

[0007] In general, according to some embodiments, multiple models are
generated based on information relating to uncertainties of model
parameters, where the models are consistent with preexisting data
regarding a subsurface structure. A system receives, on a continual
basis, information collected as an operation is performed with respect to
the subsurface structure. The multiple models are recursively sifted to
progressively select smaller subsets of the models as the collected
information is continually received.

[0008] Other or alternative features will become apparent from the
following description, from the drawings, and from the claims.

BRIEF DESCRIPTION OF THE DRAWINGS

[0009] Some embodiments are described with respect to the following
figures:

[0010] FIG. 1 is a flow diagram of a process of recursively sifting
multiple models based on information collected as an operation is
performed with respect to the subsurface structure, in accordance with
some embodiments;

[0011]FIG. 2 illustrates an example arrangement for performing a survey
operation with respect to a subsurface structure; and

[0012]FIG. 3 is a flow diagram of an uncertainty analysis workflow, in
accordance with some embodiments.

DETAILED DESCRIPTION

[0013] Traditionally, a goal of imaging a subsurface structure based on
seismic or electromagnetic (EM) survey data is to focus the data and
provide a relatively high-quality subsurface image. Later, more emphasis
was placed on delivering a proper depth image that is as close as
possible to the actual subsurface structure. To achieve the latter goal,
it may no longer be enough to simply focus the data; a realistic
anisotropic earth model should be developed to perform such imaging. An
anisotropic earth model refers to a model of the subsurface structure in
which properties of the subsurface structure differ in different
directions.

[0014] Surface seismic and/or EM data (hereinafter referred to generally
as "survey data" collected by survey receivers at or above the earth
surface) alone may not be able to uniquely resolve all the parameters of
an anisotropic subsurface structure. Often, even if well data (data
collected by well logging) is available, it still may not be possible to
resolve all the parameters of the anisotropic subsurface model.

[0015] To develop an accurate subsurface model, it is useful to understand
the impact of the uncertainty in the estimates of a velocity model and
anisotropy on the subsurface structure. This applies not only to the
depth data for a depth migration, but also the lateral positioning of
events in the subsurface image.

[0016] Even with efforts to combine multiple sources of available data,
there can still be ambiguity in subsurface models. For example, multiple
different velocity models can exist that explain observed survey data.
The result is uncertainty of the true positions of events in subsurface
images based on survey data. These uncertainties can lead to exploration
risk (e.g., trap failure), drilling risk (e.g., drying wells), and/or
volumetric uncertainties (in which there is relatively large uncertainty
in the estimated volume of subsurface fluids of interest, such as
hydrocarbons). While the underlying ambiguity may not be fully
eradicated, a quantified measure of uncertainties may provide deeper
understanding of the risks and related mitigation plans to address the
risks.

[0017] In accordance with some embodiments, uncertainty analysis
techniques are provided to allow a set of models that fit all available
data equally well to be provided to a user, such that the user is allowed
to select the most geologically plausible solution. The selection of the
most plausible model from among a set of models can be based on any a
priori information.

[0018] FIG. 1 is a flow diagram of a process according to some
embodiments. A system generates (at 102) multiple anisotropic models of a
subsurface structure based on uncertainty analysis, where the multiple
models are consistent with preexisting data regarding the subsurface
structure. The preexisting data can include surface survey data (e.g.,
seismic and/or EM survey data collected by survey receivers at or above a
surface over the subsurface structure of interest), well log data, and
other data relating to the subsurface structure.

[0019] The multiple models based on the preexisting data are associated
with ambiguity, since even though the multiple models are based on all
available sources of data relating to the subsurface structure, there can
be many different models that are consistent with the preexisting data.
The uncertainty analysis performed at 102 includes quantifying measures
of uncertainties of events (presence of various subsurface elements) in a
subsurface structure. The uncertainty analysis allows for a determination
of information relating to uncertainties of estimated model parameters.
The model ambiguity is a main cause for uncertainty of the true positions
of events in subsurface images, and these uncertainties can lead to
various risks as noted above. While the underlying ambiguity may not be
fully eradicated, quantified error measures of such uncertainties provide
deeper understanding of risks and related mitigation plans.

[0020] In some implementations, the multiple models generated (at 102)
based on the uncertainty analysis are posterior models (e.g., velocity
models that provide a velocity profile in the subsurface structure,
structural models that define structures in the subsurface structure,
etc.).

[0021] To allow a user to select from among the multiple models that are
consistent with the preexisting data, additional information is received
(at 104), where the additional information is collected on a continual
basis as an operation is performed with respect to the subsurface
structure. In some implementations, the operation that is performed with
respect to the subsurface structure includes drilling a well into the
subsurface structure, with logging performed while drilling. The logging
involves using sensors in a logging tool (positioned in the well during
drilling) to collect information regarding properties of the subsurface
structure surrounding the drilled wellbore. Receiving the additional
information on a "continual basis" means that such information continues
to be received while the operation with respect to the subsurface
structure is ongoing.

[0022] In accordance with some embodiments, the multiple models are
recursively sifted (at 106) to progressively select smaller subsets of
the multiple models as the additional information is continually
received. As the well is drilled, the logging tool continues to collect
information. The continually received information can then be used in
repeated iterations of tasks 104 and 106 to further reduce the population
of candidate models that were initially generated at 102. A determination
is made (at 108) whether a stopping criterion has been satisfied. For
example, the stopping criterion is satisfied if L or less models have
been selected at 106, where L≧1. Alternatively, the stopping
criterion is satisfied if a predefined number of iterations of 104 and
106 have been performed. If the stopping criterion has not been
satisfied, tasks 104 and 106 are repeated in the next iteration. If the
stopping criterion has been satisfied, then the FIG. 1 procedure outputs
(at 110) the selected model(s), as selected by the sifting (106).

[0023] In this manner, the number of possible models can be reduced down
to a few (e.g., one), which can then be used as the model(s) that most
accurately characterize(s) the subsurface structure.

[0024]FIG. 2 illustrates an example arrangement of performing a
land-based survey operation. Although reference is made to land-based
survey operations, it is noted that techniques according to some
implementations can also be applied to marine survey operations, where
survey equipment is provided in a body of water.

[0025] A survey source 202 (e.g., seismic source or EM source) is placed
at an earth surface 204. Also, survey receivers (e.g., seismic receivers
or EM receivers) 206 are also placed at the earth surface 204. The survey
source 202 generates survey signals that are propagated into a subsurface
structure 208. The signals are affected by or reflected by subsurface
elements in the subsurface structure 208, where the affected signals or
reflected signals are detected by the survey receivers 206.

[0026] Measurement data collected by the survey receivers 206 are provided
to a controller 210, either over a wired or wireless link. The controller
210 has an analysis module 212 executable on one or multiple processors
214. The analysis module 212 is executable to perform various tasks
according to some implementations, such as tasks depicted in FIG. 1 or
tasks discussed further below.

[0027] The processor(s) 214 is (are) connected to a storage media 216, for
storing information such as surface measurement data 218 from the survey
receivers 206. In addition, models 220, generated by the analysis module
212 according to some embodiments based on uncertainty analysis, can also
be stored in the storage media 216. As discussed in connection with FIG.
1 above, recursive sifting can be performed with respect to the models
220.

[0028] To allow for sifting from among the models 220, additional
information relating to an operation performed with respect to the
subsurface structure 208 is collected by the controller 210. As depicted
in FIG. 2, such further operation involved drilling of a wellbore 222 by
a drill string 224. The drill string 224 extends from wellhead equipment
226, and has a logging tool 228 for recording information with respect to
properties of the subsurface structure 208 during the drilling operation.
The recorded information by the logging tool 228 can be communicated to
the wellhead equipment 226, and communicated over a link 230 (wired or
wireless link) to the controller 210. The information from the logging
tool 228 is stored as well measurement data 232 in the storage media 216
of the controller 210.

[0029] To generate multiple posterior models (e.g., velocity models,
structural models, etc.) of the subsurface structure 208, an uncertainty
analysis workflow is performed, as depicted in FIG. 3. The workflow of
FIG. 3 can be performed by the analysis module 212 of FIG. 2, for
example. As depicted in FIG. 3, the uncertainty analysis workflow starts
with building (at 302) an initial anisotropy model calibrated with
available well data and steered between wells with given geological
structural interpretation. In this task, a geologically reasonable prior
distribution for the anisotropic parameters is defined; for example,
plausible geologic concepts are considered in terms of shapes and
patterns of the subsurface's anisotropic behavior. Also allowable ranges
of velocity, ε, and δ perturbations are obtained from rock
physics analysis.

[0030] Thus, a mean initial (prior) model is constructed. The prior
covariance matrix is parameterized as CP=PPT, where P is the
shaping preconditioner. In general, the initial model could be different
from the mean prior model, but in this example workflow it is assumed
they are the same. The preconditioner corresponds to a 3D smoothing
and/or steering operator with parameters defined from geologic and rock
physics considerations.

[0031] Next, multiscale non-linear tomography is performed (at 304), which
is an iterative process involving migrating the data, picking
common-image-point (CIP) gathers and dips, ray tracing, and solving a
relatively large, but sparse system of linear equations. The data vector,
Δz, corresponds to data perturbations with respect to the initial
model and can include CIP picks, checkshots, a walk-away VSP, markers and
other data types. A least-squares solver (e.g., LSQR) is applied to the
system,

[ D - 1 / 2 LP I ] Δ x ' = [
D - 1 / 2 Δ z 0 ] , ##EQU00001##

where L is the (anisotropic) tomographic operator, PΔx'=Δx is
the update vector, and Δx' is the update vector in preconditioned
space. Both update vectors include three-dimensional (3D) perturbations
for velocity, ε and δ. The obtained solution corresponds to
the minimization of the objective function, S, defined by

[0032] One of the key elements of the posterior-distribution sampling
process is the interplay between the geo-model space (defined by a
velocity, ε and δ vector) and the so-called preconditioned
space (defined such that application of the preconditioner to a vector
from this space produces the vector from the geo-model space).
Uncertainty analysis is applied after the last non-linear iteration of
tomography when the solution has converged and driven the misfit to an
acceptable, predefined value. This value could be used to recalibrate D,
and, optionally, L-curve analysis (i.e., plotting two terms from Eq. 1 as
an x-y plot in linear or logarithmic scale) could be used for this
purpose.

[0033] Next, the workflow performs (at 306) decomposition of the
anisotropic tomographic operator L produced by the tomography (304).
Further details regarding such eigen-decomposition on a Fisher
information operator is provided in U.S. Patent Publication No.
2009/0184958, referenced above. U.S. Patent Publication No. 2009/0184958
discusses techniques for updating models of a subsurface structure that
involve computing a partial decomposition of an operator that is used to
compute a parameterization representing an update of a model. More
specifically, eigen-decomposition is performed on a Fisher information
operator in the preconditioned space F=(LP)TD-1(LP) by use of
Lanczos iterations. Thus, the resulting decomposition is
F=UΛUT, where U is a matrix of eigenvectors and Λ is
the corresponding diagonal matrix of eigenvalues.

[0034] The posterior covariance matrix by definition is the inverse of the
sum of the Fisher operator and the inverse of the prior covariance
matrix. Because the prior covariance matrix in the preconditioned space
is the identity matrix, it has full rank, and thus the posterior matrix
also has full rank. Since the model vector typically has more than one
million elements, rather than explicitly storing the posterior covariance
matrix whose size is the square of the model vector, it is more practical
to store random samples of it. For this objective, two components of
Cp, the posterior covariance matrix in the preconditioned domain,
are considered. The first component is U(Λ+I)-1UT and it
corresponds to the eigen-decomposition of F (as per U.S. Patent
Publication No. 2009/0184958, referenced above). The second component is
I-UUT and it corresponds to the null-space projection operator (as
per U.S. Patent Publication No. 2009/0184958, referenced above). By
combining these two components, the following is obtained:

[0036] Here r is a random vector sampled from a unit multinormal
distribution. Application of the preconditioner to the resultant vectors
in effect maps the sample models pulled from the posterior distribution
into the geo-model space. The posterior probability for each sampled
model could be assessed by calculating objective function S by applying
Eq. 1. The resultant models are all valid solutions to the original
tomography problem: they both keep the misfit at the noise level and
satisfy the original prior information and geological constraints.

[0037] The models are then validated (at 310) by checking the predicted
residual moveout. This moveout should remain in the allowed tolerance
level, and if not, this serves as an indication of violating linearity
assumption.

[0038] The sampled posterior covariance matrix can be used for uncertainty
analysis of a model. This analysis can include the visualization and
comparison of different parts of the posterior covariance matrix, like
its diagonal, rows, and quadratic forms (in case of anisotropy). The
analysis can be performed for comparing various prior assumptions while
varying a prior covariance matrix and for comparing different acquisition
geometries.

[0039] Next, map migrations of horizons of interest are performed (at 312)
for the set of obtained perturbations in velocity, ε and δ.
The resulting set of target horizon instances is statistically analyzed
and structural uncertainty estimates are derived.

[0040] Having performed the iterative eigen-decomposition once, multiple
posterior models are derived, from which a model (or L models, where
L≧1) can be selected by performing the recursive sifting at 106
that is part of the procedure depicted in FIG. 1. Once a set of posterior
models (e.g., velocity models) have been derived, the recursive sifting
process (104, 106) can be applied to select from among the multiple
models.

[0041] In accordance with some implementations, a marker-based workflow
can be used, where the posterior models have associated horizons that
correspond to marker horizons at various depths. A "marker" refers to a
particular subsurface element, and a "marker horizon" refers to a
position of the subsurface element. In the context of some
implementations, the markers represent subterranean elements proximate a
wellbore (e.g., 222 in FIG. 2) that is being drilled. A set of marker
horizons associated with a model refer to different subsurface elements
at different depths in the subsurface structure 208.

[0042] As the wellbore is being drilled, only those models where the
corresponding marker horizons (of the models) match the actual marker
horizons within a given bound (e.g., predefined tolerance range) are
kept. Actual marker horizons are determined based on the recorded
information collected by the logging tool 228 of FIG. 2. The remaining
models (those models whose marker horizons do not match actual marker
horizons) from the initial set of posterior models are discarded. The
population of models will become smaller as each marker horizon is passed
during the drilling process. A benefit of the marker-based workflow of
sifting models is that the workflow does not require actual access to the
models. Instead, the marker-based workflow uses marker horizons
associated with the models. Maintaining and processing horizon
information involves much less storage and processing resources than
having to maintain and process the underlying models.

[0043] In alternative implementations, instead of using the marker-based
workflow, a checkshot-based workflow can be used to recursively sift
models. Checkshot involves vertical seismic profiling, where one or more
seismic sources are placed at the earth surface, and seismic receivers
are placed in a wellbore. Activation of the one or more seismic sources
at the surface causes seismic waves to be propagated through the
subsurface structure 208 to the seismic receivers in the wellbore. The
seismic waves as detected by the seismic receivers are associated with
respective travel times. In implementations in which the posterior models
are velocity models, a comparison can be made to determine whether travel
times as predicted by respective models match the actual travel times in
the checkshot. Only those models with predicted travel times that match
the checkshot time to within a predefined error range are kept, while the
remaining models are discarded.

[0044] By using some embodiments of the invention, a more accurate model
of a subsurface structure can be obtained, based on sifting among
multiple posterior models that are consistent with preexisting data.

[0045] The analysis module 212 includes machine-readable instructions
which are loaded for execution on a processor (such as processor(s) 214.
A processor can include a microprocessor, microcontroller, processor
module or subsystem, programmable integrated circuit, programmable gate
array, or another control or computing device.

[0046] Data and instructions are stored in respective storage devices,
which are implemented as one or more computer-readable or
machine-readable storage media. The storage media include different forms
of memory including semiconductor memory devices such as dynamic or
static random access memories (DRAMs or SRAMs), erasable and programmable
read-only memories (EPROMs), electrically erasable and programmable
read-only memories (EEPROMs) and flash memories; magnetic disks such as
fixed, floppy and removable disks; other magnetic media including tape;
optical media such as compact disks (CDs) or digital video disks (DVDs);
or other types of storage devices. Note that the instructions discussed
above can be provided on one computer-readable or machine-readable
storage medium, or alternatively, can be provided on multiple
computer-readable or machine-readable storage media distributed in a
large system having possibly plural nodes. Such computer-readable or
machine-readable storage medium or media is (are) considered to be part
of an article (or article of manufacture). An article or article of
manufacture can refer to any manufactured single component or multiple
components.

[0047] In the foregoing description, numerous details are set forth to
provide an understanding of the subject disclosed herein. However,
implementations may be practiced without some or all of these details.
Other implementations may include modifications and variations from the
details discussed above. It is intended that the appended claims cover
such modifications and variations.